Problem: Multiply the following complex numbers, marked as blue dots on the graph: $(1) \cdot (4 e^{3\pi i / 4})$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $1$ ) has angle $0$ and radius $1$ The second number ( $4 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius $4$ The radius of the result will be $1 \cdot 4$ , which is $4$ The angle of the result is $0 + \frac{3}{4}\pi = \frac{3}{4}\pi$ The radius of the result is $4$ and the angle of the result is $\frac{3}{4}\pi$.